‘But It Sounds the Same’: Why Audio Measurements Differ

You may recall that
we’ve been grappling
with the
measurement of audio
loudness and the implications
of the ITU’s B.S.
1770-1 standard for the
measurement of loudness,
in support of the
CALM Act.

I promised we would consider the effect
of this standard on the audio levels
we measure. Just so you know, this is background
information to add to your understanding
of a difficult topic. You don’t have
to do anything with this, except try to understand
it, sort of. Thanks.

THE NATURE OF WEIGHTING CURVES
Approximately 80 years ago, Harvey
Fletcher and Wilden Munson determined,
through measurement, that the frequency
response of human hearing varies as a function of loudness change.

This led to their creation of a set of so called
“Equal Loudness Contours,” which
show the inverse of the frequency response
of human hearing over the range
of levels that humans hear comfortably, in
10-decibel increments (anchored at 1 kHz.
and called “Phon” curves).

These Equal Loudness Contours are of
profound importance to us in audio and
acoustics. However, they are too complex
(as a data set), for easy use in measuring human
hearing or in measuring the effects of
various signals at various levels on human
hearing. As a result, simplified “weighting”
curves were derived from these contours,
to be applied in Sound Level Meters. The
primary curves are A-, B- and C-weighting.

In a simplistic, but reasonably useful
way, you can think of A-weighting as derived
from the 40 Phon Equal Loudness
Contour (derived from how we humans
hear at a level of approximately 40 dB Sound Level, which is quite soft); while
B-weighting is approximately appropriate
for the 70 Phon Contour (70 dB Sound
Level, a medium loud level for us); and Cweighting
is useful for measuring how humans
hear at around 100 dB Sound Level,
which is loud for us.

Fig. 1 shows the A-, B- and C-weighting
curves. These can be thought of as equalization
curves applied to the signal just
before it is measured (but not in the signal
path to the loudspeakers!), so that the
measurement approximates the spectrum
perceived by humans at soft, medium or
loud levels.

HOW WEIGHTING CURVES AFFECT
SIGNAL MEASUREMENT
Naturally, when
we apply such
equalization to a
signal, it affects the
overall level of the
signal as well as its
spectrum. In the
case of A-weighting,
for instance,
the bottom octave
of the spectrum
(31 Hz.) is attenuated
by 33 dB, the
second octave (63
Hz.) by 21 dB and
the third octave
(125 Hz.) by 11 dB.

This means,
for instance, that
energy in these octaves is essentially
not included in the
level measurement
of the signal. If that
part of the audio
spectrum contains
significant energy,
then the overall energy
measured will
be less than it would
be with a so-called
“broad-band” measurement.

Fig. 3 shows the approximate difference in Leq level for each weighting and excerpt, compared to broadband measurements.

So, weighted measurements
can be a
little tricky. Weighting
doesn’t just “correct
for how humans
hear,” but it also can
change the indicated
level, often by quite
a bit. Unfortunately, the
amount of change depends on the nature
of the signal, as well as the type of weighting.

In the case of B.S. 1770, the B-weighting
curve is modified (actually lowered somewhat
in frequency, letting more upper bass
be measured), and then the entire spectrum
from 2 kHz. on up is boosted by 4 dB.

The resulting curve is called “K-weighting,”
and it is the weighting that B.S. 1770-1
requires us to use for determining loudness.
Fig. 2 shows K-weighting across the
10 octaves of the audio spectrum.

USING DIFFERENT WEIGHTING
SCHEMES
To give you an idea of the effect of these
weightings, I made audio level measurements of six different audio signals: a Sine
Wave at 1 kHz.; Pink Noise; an excerpt of a
woman reading text; a solo classical piano
excerpt; a bluesy Mark Knopfler excerpt;
and a loud arena-rock excerpt.

After making broadband measurements
of Leq for each of these excerpts, I then
measured them again with A-, B-, C- and Kweighting.
The table in Fig. 3 shows the approximate
difference in Leq level for each
weighting and each excerpt, compared to
the broadband measurements.

Note that with a 1 kHz. sine wave, all the
weightings are pretty much the same (except
for the slight boost due to the highfrequency
shelf in K-weighting). For Pink
Noise, K-weighting increases the measured
level by a dB, while the other weightings
reduce it by up to 3 dB.

The spoken voice loses almost 4 dB
in level when A-weighted, but otherwise
is pretty much unaffected. The effect on
this particular classical piano excerpt
is similar. The blues ballad excerpt has a
pronounced bass track, leading to real
measurement variations with all but Cweighting.

The arena rock excerpt has lesser variations.
Note that C-weighting is pretty benign
in this regard, and doesn’t affect any
of the signals except Pink Noise very much.

Fig. 2: K-weighted response, based on a revised B-weighting curve with a 4 dB high-frequency shelf boost added. Shown using an octave band scale.

In the case of K-weighting—our real object
of interest here—the level drop from
the revised B-weighting is often offset by
the increase in high-frequency energy. In
effect, the spectrum is being tilted for measurement,
so level losses at low frequencies
are “made up” at high frequencies for
broadband signals.

WHAT IT ALL DOES AND
DOESN’T MEAN
There are several insights to be gained
from this. First, there is no such thing as unequivocal
audio level or loudness. Second,
as a matter of course, this is quite fuzzy data
and it varies as a function of time, spectrum
and weighting. Third, variations of a dB or
less are pretty much insignificant.

Finally, bass is really a wild card here and
can result in big level misreadings. (I generally
expect to find dBA noise pollution measurements
to be 6–8 dB softer than broadband
measurements of the same sound.)

Fortunately for you, K-weighting does
not generally change level very much. Be
aware, however, that you can inadvertently drive K-weighted readings up with too
much dialog or other high-frequency content
in your mix, because of that spectrum
tilt.

One final bit of advice: don’t obsess
about this. I share it with you so you can
know a little more about what is actually
going on in this very difficult aspect of audio.

Keep this information in your hip pocket for reference, but don’t drive yourself into a
froth of anxiety and control freakdom trying
to resolve the last .2 variation in dBA, or
is it dBK? Thanks for listening.

Dave Moulton keeps waiting for his
weighting to go down. Keep in mind,
you can still complain to him about almost
anything at his website,www.moultonlabs.com.